arXiv subjects

Zhenhua Zhao

Publications and source records attributed to Zhenhua Zhao.

6 recordsLinked to original sources

arXiv2026

Optimal Weighted $L^2$ Hessian Estimates for Parabolic Equations under General Diffusion Marginals

We study weighted $L^2$ Hessian estimates for parabolic terminal equations under diffusion marginals. The reference diffusion determines the norm, and its generator may have different principal coefficients from the PDE. We characterize the limiting optimal Hessian constant uniformly over shrinking subintervals of a fixed time horizon, with zero terminal data. Under coefficient regularity, uniform ellipticity and bounded reference drift, finiteness characterizes linear well-posedness in the weighted parabolic Sobolev space on the full interval. For initial laws satisfying weighted doubling and coercivity conditions, the constant is the maximum of initial, flat and exponential-mixture contributions. Additional geometric regularity and nonnegative Ricci curvature identify the full mixture contribution, including spatial infinity, through terminal momenta of paths minimizing action plus the initial potential. In the matching case, with reference covariance $a$, PDE matrix $a/2$ and normalized Hessian $a^{1/2}D^2u\,a^{1/2}$, the constant is $2$ with time weight $t^α$, $α\ge1/2$, for every initial law; point starts attain $2\sqrt2$ at $α=0$.

math.PR↗

arXiv2026

A Deep Second-Order Stochastic Residual Method for Fully Nonlinear Parabolic PDEs

We introduce the Deep Second-Order Stochastic Residual Method (D2SRM) for high-dimensional, Hessian-dependent fully nonlinear parabolic PDEs. A single scalar space--time network generates derivative-consistent approximations of the solution, gradient, and Hessian, which are trained jointly through second-order Brownian one-step residuals and terminal value and gradient penalties. For globally Lipschitz equations with identity diffusion and sufficiently weak Hessian coupling, we establish well-posedness in a Brownian occupation space and develop a population-level convergence theory. Under additional regularity, an a posteriori estimate bounds the squared full-jet occupation error of any admissible candidate by the time step and its population objective. For approximate population minimizers, the error bound separates time discretization, neural approximation, and population suboptimality; when the latter two terms are $O(h)$, the full-jet occupation norm is $O(h^{1/2})$. Experiments on a 100-dimensional manufactured benchmark compare terminal treatments, probe Hessian couplings inside and outside the proved small-gain range, and show decreasing errors as the time step decreases. The code is available at https://github.com/ZZHPKU/D2SRM.

math.NA↗

arXiv2025

FPT-Noise: Dynamic Scene-Aware Counterattack for Test-Time Adversarial Defense in Vision-Language Models

Vision-Language Models (VLMs), such as CLIP, have demonstrated remarkable zero-shot generalizability across diverse downstream tasks. However, recent studies have revealed that VLMs, including CLIP, are highly vulnerable to adversarial attacks, particularly on their visual modality. Traditional methods for improving adversarial robustness, such as adversarial training, involve extensive retraining and can be computationally expensive. In this paper, we propose a new Test-Time defense: Feature Perception Threshold Counterattack Noise (FPT-Noise), which enhances the adversarial robustness of CLIP without costly fine-tuning. Our core contributions are threefold: First, we introduce a Dynamic Feature Modulator that dynamically generate an image-specific and attack-adaptive noise intensity parameter. Second, We reanalyzed the image features of CLIP. When images are exposed to different levels of noise, clean images and adversarial images exhibit distinct rates of feature change. We established a feature perception threshold to distinguish clean images from attacked ones. Finally, we integrate a Scene-Aware Regulation guided by a stability threshold and leverage Test-Time Transformation Ensembling (TTE) to further mitigate the impact of residual noise and enhance robustness.Extensive experimentation has demonstrated that FPT-Noise significantly outperforms existing Test-Time defense methods, boosting average robust accuracy from 0.07% to 56.86% under AutoAttack while maintaining high performance on clean images (-1.1%). The code will be made public following the publication of the study. The code will be made public following the publication of the study.

cs.CR↗

arXiv2025

Effect of Attachment Surface on Biofilm Response and the Dissipation of PAHs and nitrogen in Submerged Plant System under the application of Bactericide and Algaecide

The biofilms response on active attachment surfaces (submerged plant leaves) and inert attachment surfaces (biomimetic plant glass attachment surfaces) and their effects on PAHs and nitrogen transformation under the application conditions of bactericide, algaecide and PAHs were investigated by lab simulated hydroponics and high-throughput molecular biology methods in Vallisneria natans (VN), Hydrilla verticillata (HV) and biomimetic plants (BP) systems. Results showed that the introduction of bactericide, algaecide and PAHs changed the microorganism composition in biofilm, the presence or absence of submerged plants was the primary factor causing differences in microbial communities. Moreover, the microbial diversity and endemic species of biomimetic plant biofilms were higher than those of submerged plant systems, indicating that submerged plants have selectively induced the reconstruction of biofilm-leaves. The introduction of bactericide, algaecide and PAHs leads to abnormal accumulation of TP and NH3-N in overlying water, as well as NO3-N and TP content in sediment. However, submerged plants can weaken and alleviate the stress effects of these factors on nitrogen and phosphorus conversion. Compared to the inert biomimetic plant glass surface, the presence of active surfaces in submerged plants results in a much higher abundance of PAHs degrading bacteria (Sphingomonas and Novosphingobium) and nitrogen converting bacteria (e.g. denitrifying bacteria of Methylophilus, Methylotenera, Flavobacterium, Hydrogenophaga, Aquabacterium, and nitrogen-fixing bacteria of Rhizobium, Azoarcus, Rhizobacter, Azonexus) in biofilm-leaves of submerged plants after the addition of bactericide, algaecide and PAHs. Coupled degradation of PAHs and nitrogen occurs, which is beneficial for the treatment of combined pollution caused by PAHs and nitrogen.

q-bio.CB↗

arXiv2025

Face processing emerges from object-trained convolutional neural networks

Whether face processing depends on unique, domain-specific neurocognitive mechanisms or domain-general object recognition mechanisms has long been debated. Directly testing these competing hypotheses in humans has proven challenging due to extensive exposure to both faces and objects. Here, we systematically test these hypotheses by capitalizing on recent progress in convolutional neural networks (CNNs) that can be trained without face exposure (i.e., pre-trained weights). Domain-general mechanism accounts posit that face processing can emerge from a neural network without specialized pre-training on faces. Consequently, we trained CNNs solely on objects and tested their ability to recognize and represent faces as well as objects that look like faces (face pareidolia stimuli).... Due to the character limits, for more details see in attached pdf

cs.CV↗

arXiv2005

Topological quantization of self-dual Chern-Simons vortices on Riemann Surfaces

The self-duality equations of Chern-Simons Higgs theory in a background curved spacetime are studied by making use of the U(1) gauge potential decomposition theory and $ϕ$-mapping method. The special form of the gauge potential decomposition is obtained directly from the first of the self-duality equations. Using this decomposition, a rigorous proof of magnetic flux quantization in background curved spacetime is given and the unit magnetic flux in curved spacetime is also found . Furthermore, the precise self-dual vortex equation with topological term is obtained, in which the topological term has always been ignored.

hep-th↗